Equations of Motion

A stone is thrown with an initial speed of $4.9 \mathrm{m} {\mathrm{s}}^{-1}$ from a bridge in a vertical upward direction. It falls down in water after $2$ seconds. The height of the bridge is _____.

A force act on mass $1.5 \mathrm{kg}$ at rest for $0.5 \mathrm{s}$ after force stop acting object travel a distance of $5 \mathrm{m}$ in $2 \mathrm{s}$. Hence, magnitude of acceleration of object will be

A particle starts with a velocity of $5 {\mathrm{ms}}^{-1}$ and moves with a uniform acceleration of $2.5 {\mathrm{ms}}^{-2}$ its velocity after $4 \mathrm{s}$ is

 A player throws a ball upward with initial speed of $29.4 \mathrm{m}/\mathrm{s}$. The time taken by ball to return to player's hand is

A packet is dropped from a balloon which is going upwards with the velocity $12 \mathrm{m}/\mathrm{s}$, the velocity of the packet after $2 \mathrm{seconds}$ will be?

A ball is thrown vertically upwards and reaches a maximum height in $3 \mathrm{s}$, find the velocity with which it was thrown upwards, and the maximum height attained by the ball? 
(Take $g=10 \mathrm{m}/{\mathrm{s}}^2$) 

An object is travelling with velocity 'v'. The brakes are applied and the car stops at a distance 's'. If the velocity of car is 2v, then at what distance the car will stop?

A ball is dropped from the top of a tower $40 \mathrm{m}$ high. What is its velocity when it has covered a distance of $20 \mathrm{m}$? What would be its velocity when it hits the ground?

Take, $g=10 \mathrm{m} {\mathrm{s}}^{-2}$.

A shot travelling at the rate of $120 \mathrm{m}/\mathrm{s}$ just able to pierce 8 cm thick. What velocity is required to pierce a plank of $15 \mathrm{cm}$ thick?

What are equations of motion?

A body is thrown vertically upwards with an initial velocity of $9.8 {\mathrm{ms}}^{-1}$. What is its speed and direction after (a) one second  (b) 2 seconds. Find the height to which it will rise ($\mathrm{g}=9.8 {\mathrm{ms}}^{-2}$).

A stone was thrown upwards with a velocity of $56.6 \mathrm{m}/\mathrm{s}$ from a cliff. If the height of the cliff is $243 \mathrm{m}$, what is the velocity of the stone when it hits the ground? Assume that air resistance is negligible. $\left(g=9.81 \mathrm{m}/{\mathrm{s}}^2\right)$

A body covers a distance of $8.4 \mathrm{m}$ with acceleration $5 \mathrm{m} {\mathrm{s}}^{-2}$ and velocity $10 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate the initial velocity of the body.

A motorcycle starts its motion with constant acceleration $10 \mathrm{m} {\mathrm{s}}^{-2}$ from rest and moves for $5$seconds. Now he stops accelerating the motorcycle and continues to move with the constant velocity he achieved at that instant for another $5$ seconds. Now he applies break which generates retardation of $5 \mathrm{m} {\mathrm{s}}^{-2}$ and moves in this state for $2$ seconds. Find the total distance travelled by the motorcycle.

A body is dropped from certain height $\mathrm{H}$. If the ratio of the distances travelled by it in $\left(\mathrm{n}-3\right)$ seconds to ${\left(\mathrm{n}-3\right)}^{\mathrm{th}}$ second is $4:3$, find $\mathrm{H}$. (Take $\mathrm{g}=10 {\mathrm{ms}}^{-2}$)

A force of $6 \mathrm{N}$ acts on a body at rest and of mass $1 \mathrm{kg}$, During this time, the body attains a velocity of $30 \mathrm{m} {\mathrm{s}}^{-1}$. Calculate the time for which the force acts on the body.
 

A body is dropped from a balloon which is moving upward with a speed of $10 \mathrm{m}/\mathrm{s}$. The body is dropped when the balloon is at a height of $390 \mathrm{m}$ from the surface of the earth. Find the approximate time taken by the body to reach the surface of the earth. Take $g=10 \mathrm{m}/{\mathrm{s}}^2$. 

A spacecraft is flying in a straight path and it has a velocity of $100 \mathrm{km} {\mathrm{s}}^{-1}$ fires its rocket motors for $8.0 \mathrm{s}$. At the end of this time, its velocity increases and becomes $140 \mathrm{km} {\mathrm{s}}^{-1}$ Find the distance travelled by the spacecraft in the first $12 \mathrm{s}$ after the motors were started? The motors were in action for only $8.0 \mathrm{s}$.

Derive all the three equations of motion from velocity-time graph.

When brakes are applied, the speed of a train decreases from $198 \mathrm{km} {\mathrm{h}}^{-1}$ to $90 \mathrm{km} {\mathrm{h}}^{-1}$ in $1000 \mathrm{m}$. How much further will the train move before coming to rest? (Assuming the retardation to be constant). Also find the time taken by the train to stop after the application of brakes.